My ex and I sat in different rooms too. Court ordered he was not be be around me or talk directly to me. I could have allowed it but didn't because I didn't want to see him. He is a very angry person and I was not about to take a blunt hit from him.
Our lawyers did the fighting, I was tired of fighting.
I walked away with everything I wanted. I gave in on the little things like pick up time and drop off times but other than that I stood my ground on the important issues ( GF being babysitter on his weekends, drinking issues, sleeping arrangements ect..)
It can work for some people but other need a judge take the reins. My ex didn't want to go to court (his lawyer charges extra for court hearings) so he caved. I was more than willing to sit in front of a judge.

Don't know if mediation works the same everywhere as it does in Washington.
It involved a judge telling us both some facts and then separating us into different rooms to work out any issues. Both of us were able to agree or not without actually hearing from the other. Neither one of us got 100% of what we wanted but I walked away feeling as if things worked out very fair. Pushing for the little I didn't get would have cost more in court/Lawyer fees then it would have been worth.

Actually I got a good laugh that day as the Judge told me EX's lawyer Yelled at him (ex) because he was being unreasonable.

My advice: Have someone waiting outside for you. It will be a rough day emotionally regardless of the outcome. My best friend drive 3 hours to be with me that day. Meant the world to me.